EFFECT OF AN IN-PLANE MAGNETIC FIELD ON THE INTERLAYER TRANSPORT OF QUASIPARTICLES IN LAYERED SUPERCONDUCTORS

The symmetry of the excitation gap in the superconducting and normal state of the cuprates, the quasi-twodimensional organic salts, and the ruthenate oxides has been the focus of theoretical and experimental studies for the last several years. Now there is consensus that most of the cuprates are not only anomalous metals that develop a pseudogap when underdoped [1], but also that they are unconventional (d-wave) superconductors with nodes on the Fermi surface, as demonstrated in phasesensitive Josephson junction experiments [2]. The situation is less clear in the organic salts and the ruthenates, in spite of many reports of power laws in the temperature behavior of various transport and thermodynamic properties (see, e.g., Refs. [3,4]). Spin fluctuation models for the organics predict a dxy superconducting state similar to the cuprates [4,5]. Since phase-sensitive Josephson junction and angle-resolved photoemission spectroscopy experiments are not available for these materials, other more stringent experiments are required. In this Letter we propose angle-dependent magnetoresistance oscillation (AMRO) experiments which directly probe the locations of the line nodes of the gap in the quasiparticle excitation spectrum in the superconducting phase or in the normal state with a pseudogap. We show that in highly anisotropic layered materials the dependence of the quasiparticle c-axis I-V characteristics on the orientation of a magnetic field parallel to the layers, Bk , allows one to extract the momentum dependence of the gap function. In particular, we calculate the quasiparticle c-axis conductivity, σq, in Josephson coupled layered gapless superconductors (e.g., d-wave or p-wave pairing) as a function of Bk = (Bx, By) and compare it with results for s-wave pairing. We assume a significant contribution of coherent electron tunneling between adjacent layers. The condition for coherent tunneling in the presence of an in-plane magnetic field requires |δk| ≪ |b|, where |δk| is the change of the in-plane momentum of a tunneling electron, where b = (2πs/�0)(By, −Bx), and s is the interlayer spacing. We show that under such conditions the dependence of σq on the orientation of b enables one to determine whether the superconducting gap (or any other kind of gap) has nodes on the Fermi surface, as well as information on the location of these nodes. The conditions that are necessary to apply our method seem to be fulfilled in highly anisotropic and very clean organic salts like the quasi-two-dimensional BEDT-TTF [bis(ethylenedithio)-tetrathiafulvalene] superconductors [4], the Bi- or Tl-based cuprates [6,7], and the oxide superconductor Sr2RuO4 [8]. For perfect crystals with translational invariance we use the interlayer Hamiltonian, which describes the conservation of the in-plane momentum when electrons tunnel between the layers. In Josephson coupled superconducting layers the in-plane magnetic field penetrates almost freely into the sample, inducing the vector potential